Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey) aluminum conductor alloy doped with galliumIzatullo N Ganiev1 Firdavs A Aliev2 Haydar O Odinazoda3 Ahror M Safarov1 Jamshed H Jayloev1

1 V I Nikitin Institute of Chemistry Academy of Sciences of the Republic of Tajikistan 2992 Sadriddin Ayni Str Dushanbe 734063 Tajikistan2 Dangarinsk State University 25 Markazi Str Dangara 735320 Tajikistan3 Tajik Technical University named after academician MS Osimi 10 Radjabovs Str Dushanbe 734042 Tajikistan

Corresponding author Izatullo N Ganiev (ganiev48mailru)

Received 15 August 2019 diams Accepted 29 December 2019 diams Published 30 March 2020

Citation Ganiev IN Aliev FA Odinazoda HO Safarov AM Jayloev JH (2020) Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey) aluminum conductor alloy doped with gallium Modern Electronic Materials 6(1) 25ndash30 httpsdoiorg103897jmoem6155277

AbstractAluminum is a metal having permanently broadening applications Currently aluminum and its alloys successfully replace conventional metals and alloys in a number of application fields The wide use of aluminum and its alloys is primarily stipulated by its advantageous properties eg low density high corrosion resistance and electrical conductiv-ity as well as the possibility of applying protective and decorative coatings In combination with great abundance and relatively low cost which has been almost constant in recent years this permanently broadens the application range of aluminum The electrochemical industry is one of the promising application fields of aluminum The E-AlMgSi type (Aldrey) conductor aluminum alloy has high strength and ductility This alloy acquires high electrical conductivity upon appropriate heat treatment Products made from it are used almost exclusively for overhead power lines This work presents data on the temperature dependence of heat capacity heat conductivity and thermodynamic functions of the E-AlMgSi (Aldrey) aluminum alloy doped with gallium The studies have been carried out in ldquocoolingrdquo mode

It has been shown that with an increase in temperature the heat capacity and thermodynamic functions of E-AlMgSi (Aldrey) alloy doped with gallium increase while the Gibbs energy decreases Gallium doping to 1 wt reduces the heat capacity enthalpy and entropy of the initial alloy and increases the Gibbs energy

Keywordsaluminum E-AlMgSi (Aldrey) alloy gallium heat capacity heat conductivity ldquocoolingrdquo mode enthalpy entropy Gibbs energy

1 Introduction

Aluminum and its alloys are widely used in electrical engineering as conductor and structural materials As a conductive material aluminum is characterized by high electrical and thermal conductivity (after copper the

maximum level among all technically used metals) Alu-minum also has a low density high atmospheric corrosi-on resistance and resistance to chemicals

Another advantage of aluminum is its neutrality to insulators eg oils lacquers and thermoplastics inclu-ding at high temperatures Aluminum differs from other

copy 2020 National University of Science and Technology MISiS This is an open access article distributed under the terms of the Creative Commons Attribution License (CC-BY 40) which permits unrestricted use distribution and reproduction in any medium provided the original author and source are credited

Modern Electronic Materials 2020 6(1) 25ndash30DOI 103897jmoem6155277

Research Article

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)26

metals by a low magnetic permeability and the formation of a non-conductive easily removable powdered product (Al2O3) in the electric arc [1ndash3]

The use of aluminum and its alloys for the manufactu-ring of switching devices power transmission line poles cases of electric motors and switches etc is regulated by special guidelines or general design rules

The economic feasibility of using aluminum as a con-ductive material is explained by the favorable ratio of its cost to the cost of copper In addition one should take into account that the cost of aluminum has remained virtually unchanged for many years [4ndash6]

When using conductive aluminum alloys for the manu-facture of thin wire winding wire etc certain difficulties may arise in connection with their insufficient strength and a small number of kinks before fracture

One method to increase the strength of aluminum al-loys is doping Doping elements should be chosen so as to provide an increase in alloy strength while retaining suf-ficiently high electrical conductivity Most of impurities increase the strength of aluminum but reduce its electrical conductivity One can chose impurities which improve the mechanical properties of aluminum while reducing its electrical conductivity but slightly and introduce them aiming to increase the strength of aluminum

Aluminum alloys have been developed in recent years which even in a soft state have strength characteristics that allow them to be used as a conductive material [4ndash6]

Silicon doping gives the best results However the strength of this alloy in a hardened state is insufficient A successful combination of high mechanical strength and electrical conductivity can be achieved by producing ter-nary and more complex composition aluminum alloys with silicon magnesium iron and other elements Special heat treatment of these alloys provides for the desired results These alloys and collectively referred to as Aldrey [1ndash3]

One well-known Aldrey alloy is aluminum with the following impurities 03ndash05 Mg 04ndash07 Si and 02ndash03 Fe The compulsory impurities which determi-ne the advantageous properties of Aldrey are magnesium and silicon whose concentration ratio should meet the formula of the Mg2Si compound forming in the alloy and acting as a hardening agent that delivers the good mecha-nical properties However practical applications should be designed taking into account that the alloy always contains iron which is a still unavoidable yet often detri-mental impurity in any technical grade of aluminum that forms a silicon containing compound (Al6Fe2Si3) There-fore in order to provide for the formation of the Mg2Si compound one should dope the alloy with a certain excess of silicon (04ndash05) compared with its theoretically re-quired amount [1ndash3]

The hardening action of the Mg2Si compound is ac-counted for by the fact that its solubility in solid alumi-num declines with a decrease in temperature For example the maximum Mg2Si solubility in aluminum at 595 degC is 185 while at 200 degC this figure is only 02 Therefore if an Aldrey type alloy is heated to above 500 degC (at this

temperature all the Mg2Si is in the solid solution) and ra-pidly cooled (quenched) a supersaturated Mg2Si solution in aluminum is produced [1ndash3]

Long-term resting of the alloy leads to the precipitation of excess Mg2Si from the solid solution in the form of a fine-grained component which increases the mechani-cal strength of the alloy (precipitation hardening) This resting of alloy is referred to as natural aging The effect delivered by aging can be accelerated and amplified by slightly heating the alloy (to 150ndash200 degC) ie applying artificial aging During aging the Mg2Si impurity precipi-tates from the solid solution and increases the electrical conductivity of the alloy [1ndash3]

The heat treatment process route of Aldrey type alloy wire includes water quenching of rolled or pressed wire at 510ndash550 degC followed by drawing and artificial aging at 140ndash180 degC [1ndash3]

The tensile strength of Aldrey is two times higher than that of aluminum Given the same electrical conductivity this provides for a 15 times higher strength of Aldrey wire than that of copper wire with a two times smaller specific weight This advantage allows one to increase the pole spans of power transmission lines The higher hardness of Aldrey reduces the risk of wire damage during installation in comparison with aluminum or steel-aluminum

The aim of this work is to study the effect of galli-um doping on the thermophysical properties and ther-modynamic functions of E-AlMgSi (Aldrey) aluminum conductor alloy with the 05 wt Si and 05 wt Mg chemical composition

2 Experimental

The alloys were synthesized in a SShOL type resistance laboratory shaft furnace at 750ndash800 degC A6 grade alu-minum which was additionally doped with the calcu-lated amount of silicon and magnesium was used as a charge in the preparation of the E-AlMgSi alloy When doping aluminum with silicon the metallic (01 wt) silicon present in primary aluminum was taken into ac-count Magnesium wrapped in aluminum foil was in-troduced into the molten aluminum using a bell The metallic gallium was introduced into the melt in a form wrapped in aluminum foil The alloys were chemical-ly analyzed for silicon and magnesium contents at the Central Industrial Laboratory of the State Unitary En-terprise Tajikistan Aluminum Company The alloy com-positions were controlled by weighing the charge and the alloys Synthesis was repeated if the alloy weight deviated from the target one by more than 1ndash2 relu Then the alloys were cleaned from slag and cast into graphite molds in order to obtain samples for thermop-hysical study The cylindrical samples had a diameter of 16 mm and a length of 30 mm

The cooling rate was determined by plotting cooling curves for the samples The cooling curves were sample temperature dependences on time of cooling in air [7ndash15]

Modern Electronic Materials 2020 6(1) 25ndash30 27

The process of heat transfer from a hotter body to a colder one tends to establish a thermodynamic equilibri-um in a system consisting of an extremely large number of particles Therefore this is a relaxation process which can be described by an exponential function of time In the case in question the heated body transfers heat to the environment ie a body having an infinitely large heat capacity The ambient temperature can therefore be ta-ken to be constant (T0) Then the body temperature de-pendence on time τ can be written in the following form ∆T = ∆T1e

-ττ1 where ∆T is the difference between the tem-peratures of the heated body and the environment ∆T1 is the difference between the temperatures of the heated body and the environment at τ = 0 τ1 is the cooling con-stant which is equal to the time during which the differen-ce between the temperatures of the heated body and the environment decreases by e times

Schematic of the heat capacity measurement unit used in our experiment is shown in Fig 1 The electric furnace 3 is movably mounted on the platform 6 along which it can move up and down on thread The sample 4 and the stan-dard 5 which are also movable are in the form of 30 mm long 16 mm diam cylinders with channels drilled out in the butt ends in which thermocouples are inserted The ends of the thermocouples are connected to a Digital Mul-timeter DI9208L multichannel digital thermometer (7) The electric furnace 3 is powered on from the laboratory transformer 1 after setting the required temperature with the thermocontroller 2 The initial temperature is read on the multichannel digital thermometer 7 The sample 4 and the standard 5 are put into the electric furnace 3 and heated to the required temperature the latter being conrtolled with the multichannel digital thermometer 7 and the PC 8 The sample 4 and the standard 5 are simultaneously removed from the electric furnace 3 following which the tempera-ture is recorded The readings of the multichannel digital thermometer 7 are recorded with the PC 8 at 5 10 and 20 sec intervals until the sample and the standard cool down

The multichannel digital thermometer used for tempe-rature measurements allowed PC recording of measure-

ment results in a tabular form The temperature measure-ment accuracy was 01 degC the temperature recording time interval being 1 sec The relative temperature measure-ment error in the 40 to 400 degC was plusmn1 The heat capa-city measurement error for this method was within 4ndash6 depending on temperature

The measurement results were processed with MS Ex-cel and data charts were built with Sigma Plot The corre-lation coefficient was Rcorr gt 0999 confirming the correct choice of approximating function

3 Results and discussion

The experimental temperature vs time curves of the sam-ples (Fig 2) can be described with an equation of the fol-lowing type

b kT ae pe (1)

where a b p and k are constants and τ is the cooling timeDifferentiating Eq (1) with respect to τ we obtained

the following sample cooling rate equation

(2)

From Eq (2) we calculated the cooling rates of the E-AlMgSi (Aldrey) alloy samples doped with gallium (Fig 3) The values of the a b p k ab and pk coef-ficients in Eq (2) for the test alloys are summarized in Table 1

Table 1 a b p k ab and pk coefficients in Eq (2) for E-AlMgSi (Aldrey) alloy with gallium

Gallium content in E-AlMgSi (Aldrey) alloy wt

a К b 10-3 s-1

p K k 10-5 s-1

ab 10-1 Ks

pk 10-3 Ks

0 16561 446 31472 227 738 714005 17218 455 31499 220 783 69201 15914 471 31485 202 749 63505 15382 464 31399 181 713 56710 159234 473 31517 210 754 662Standard (Al Grade A5N) 49426 501 31992 257 025 823

Figure 1 Solid body ldquocoolingrdquo mode heat capacity measurement unit 1 automatic transformer 2 thermocontroller 3 electric fur-nace 4 sample 5 standard 6 electric furnace platform 7 multichannel digital thermometer and 8 recording device (PC)

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)28

Then based on the calculated alloy cooling rates and using Eq (3) we determined the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gallium and the standard (Al Grade A5N)

P PC Cmm

dTddTd

0 0 1

2

1

2

2 1= sdot

τ

τ

(3)

where m1 = ρ1V1 is the standard weight m2 = ρ2V2 is the test sample weight are the cooling rates of the al-loy and standard samples at the specific test temperature

Applying a polynomial regression we obtained the tem-perature dependence equation of the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gallium

(4)

The values of the а b c and d coefficients in Eq (4) are summarized in Table 2

Results of heat capacity calculations for the alloys using Eq (3) for different temperatures are summarized in Table 3 The heat capacity of the alloys increases with an increase in the gallium concentration in the E-AlMgSi (Aldrey) alloy and temperature Using the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gal-lium and the experimental data on the cooling rate we cal-culated the temperature dependence of the heat conducti-vity coefficient of the E-AlMgSi (Aldrey) alloy using the following equation

0

0

STTdd TmC

aP

(5)

where Т and Т0 are the sample and environment tempera-tures respectively and S and m are the surface area and weight of the sample The temperature dependences of the heat conductivity coefficient for the E-AlMgSi (Ald-rey) alloy doped with gallium are shown in Fig 4

To calculate the temperature dependence of the ent-halpy H entropy S and Gibbs energy G we used integral specific heat capacities (Eq 4)

)(4

)(3

)(2

)() ]()([ 40

430

20

200

00 TTdTTcTTbTTaTHTH (6)Figure 3 Temperature dependences of cooling rate for (1) stan-dard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium contents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Table 2 Values of the a b c and d coefficients in Eq (4) for samples of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey) alloy wt

а b с d R J(kgmiddotK) J(kgmiddotK 2) J(kgmiddotK 3) J(kgmiddotK 4)

0 -1039496 8430 021 171 09925005 -1039496 8290 -020 166 0989901 -1378822 10685 -026 211 0995005 -1946350 15221 -038 315 0998010 -1014732 7849 -019 151 09989Standard (Al Grade A5N) 64588 036 0 0 10

R is the correlation coefficient

Figure 4 Temperature dependences of heat conductivity co-efficient for (1) standard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium con-tents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Figure 2 Temperature as a function of cooling time for (1) standard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium contents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Modern Electronic Materials 2020 6(1) 25ndash30 29

)(3

)(2

)(l n) ]()([ 30

320

20

00

00 TTdTTcTTbTTaTSTS (7)

)]()([) ]()([) ]()([ 000

000

000 TSTSTTHTHTGTG (8)

where T0 = 29815 KResults of enthalpy entropy and Gibbs energy calcula-

tions using Eqs (6)ndash(8) with a 25 K step are summarized in Table 4

Table 3 Temperature dependence of specific heat capacity (kJ(kgmiddotK)) of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey) alloy wt 0

0PC kJ(kg middot K)

300 K 325 K 350 K 375 K 400 K 450 K0 75100 85536 90762 92383 92000 91637005 67855 79412 85813 88615 89372 9098001 57454 73123 82021 86125 87413 8945505 53177 71259 80269 83160 82886 8465310 53162 65839 73381 77205 78726 80520Standard (Al Grade A5N) 85462 87790 90155 92545 94948 99746

Table 4 Temperature dependences of thermodynamic functions of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey)

alloy wt

Thermodynamic Functions 300 K 325 K 350 K 375 K 400 K 450 K

[H 0(T ) ndash H 0 (T0) ] kJkg for alloys

0 13799 215847 437138 666654 897383 1354471005 12451 197762 405196 623809 846546 129562601 11125 184786 389238 609993 837508 129937205 09674 167417 358409 563663 771572 118585210 09726 159695 334642 523503 718750 1115986Standard (Al Grade A5N) 15795 232351 454777 683149 917514 1404266[S 0(T ) ndash S 0 (T0

) ] kJ(kgmiddotK) for alloys0 00046 00692 01348 01982 02577 03654005 00042 00634 01248 01852 02427 0348401 00037 00592 01198 01807 02394 0348205 00033 00536 01102 01669 02205 0318110 00033 00512 01030 01551 02055 02991Standard (Al Grade A5N) 00053 00746 01405 02035 02640 03786[G 0(T ) ndash G 0 (T0

) ] kJkg for alloys0 -00043 -09209 -34739 -76429 -133499 -289837005 -00038 -08394 -31931 -70741 -124299 -27254901 -00034 -07732 -30065 -67655 -120232 -26757605 -00031 -06922 -27354 -62028 -110526 -24559510 -00030 -06705 -25947 -58237 -103367 -229901Standard (Al Grade A5N) -00049 -10111 -37068 -80133 -138629 -299625T0 = 29815 K

Figure 5 Microstructure (times650) of E-AlMgSi (Aldrey) alloy (a) pure and (bndashe) doped with gallium wt (a) 0 (b) 005 (c) 01 (d) 05 and (e) 10

c

a

e

b

d

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)30

The increase in the enthalpy entropy and Gibbs energy of the E-AlMgSi (Aldrey) alloy upon gallium doping can be accounted for by an increase in the heterogeneity of the structure of the alloys [16ndash18] As can be seen from Fig 5d e the microstructure of the E-AlMgSi (Ald-rey) alloy containing 05 and 10 wt gallium does not exhibit primary Mg2Si precipitates In the initial alloy (Fig 5a) and low-gallium alloys (Fig 5b c) the Mg2Si phase precipitates crystallize in a needle-shaped form in the aluminum solid solution matrix

4 Conclusion

The heat capacity of the AlMgSi (Aldrey) alloy doped with gallium was determined in ldquocoolingrdquo mode based

on the known heat capacity of a A5N aluminum stan-dard Using the obtained polynomial dependences we showed that with an increase in temperature the heat ca-pacity enthalpy and entropy of the alloys increase and the Gibbs energy decreases Gallium doping within the experimental concentration range (005ndash10 wt) redu-ce the heat capacity enthalpy and entropy of the initial AlMgSi (Aldrey) alloy but increase the Gibbs energy The increase in the heat capacity heat conductivity en-thalpy and entropy of the alloys with gallium content is accounted for by the modifying action of gallium on the structure of the α-Al solid solution and hence an in-crease in the heterogeneity of the structure of the multi-component alloys

References1 Usov VV Zaimovsky AS Provodnikovye reostatnye i kontaktnye

materialy Materialy i splavy v elektrotekhnike [Conductor rheostat and contact materials Materials and alloys in electrical engineering] Vol 2 Moscow Leningrad Gosenergoizdat 1957 184 p (In Russ)

2 Alyuminievye splavy svoistva obrabotka primenenie [Aluminum alloys properties processing application] Moscow Metallurgy 1979 679 p (In Russ)

3 Alieva SG Altman MB Ambartsumyan SM et al Promyshlen-nye alyuminievye splavy Spravochnik [Industrial aluminum alloys Handbook] Moscow Metallurgy 1984 528 p (In Russ)

4 Beleskiy VM Krivov GA Alyuminievye splavy (Sostav svoistva tekh-nologiya primenenie) [Aluminum alloys (Composition properties technology application)] Kiev KOMITEKh 2005 365 p (In Russ)

5 Chlistovsky RM Heffernan PJ DuQuesnay DL Corrosion-fatigue behaviour of 7075-T651 aluminum alloy subjected to periodic over-loads Internat J Fatigue 2007 29(9ndash11) 1941ndash1949 httpsdoiorg101016jijfatigue200701010

6 Luts AR Suslina AA Alyuminii i ego splavy [Aluminum and its alloys] Samara Samara State Technical University 2013 81 p (In Russ)

7 Niezov KhKh Ganiev IN Berdiev AE Splavy osobochistogo al-yuminiya s redkozemelrsquonymi metallami [Alloys high purity alumin-ium with rare-earth metals] Dushanbe Sarmad kompaniya 2017 146 p (In Russ)

8 Berdiev AE Ganiev IN Niyozov HH Obidov FU Ismoilov RA Influence of yttrium on the anodic behavior of the alloy AK1M2 Iz-vestiya vuzov Izvestiya vuzov Materialy elektronnoi tekhniki = Ma-terials of Electronics Engineering 2014 17(3) 224ndash227 (In Russ) httpsdoiorg10170731609-3577-2014-3-224-227

9 Ganiev IN Mulloeva NM Nizomov Z Obidov FU Ibragimov NF Temperature dependence of the specific heat and thermodynam-ic functions of alloys of the Pb-Ca system High Temperature 2014 52(1) 138ndash140 httpsdoiorg101134S0018151X1401009X

10 Ganiev IN Mulloeva NM Nizomov ZA Makhmadulloev HA Heatphyscal properties and thermodynamic functions alloys of Pb-Sr system Izvestiya Samarskogo nauchno tsentra Rossiiskoi Aka-demii nauk = Izvestia of Samara Scientific Center of the Russian

Academy of Sciences 2014 6(6) 38ndash42 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_6_38_42pdf

11 Ibrokhimov NF Ganiev IN Nizomov Z Ganieva NI Ibrokh-imov SZh Effect of cerium on the thermophysical properties of AMg2 alloy The Physics of Metals and Metallography 2016 117(1) 49ndash53 httpsdoiorg101134S0031918X16010063

12 Ganiev IN Yakubov USh Sangov MM Safarov AG Calcium influence upon the temperature dependence of specific heat capacity and on changes in the thermodynamic functions of aluminum alloy AlFe5S10 Vestnik tekhnologicheskogo universiteta = Bulletin of the Technological University 2018 21(8) 11ndash15 (In Russ)

13 Ibrohimov SZh Eshov BB Ganiev IN Ibrohimov NF Influence scandium on the physicochemical properties of the alloy AMg4 Iz-vestiya Samarskogo nauchno tsentra Rossiiskoi Akademii nauk = Izvestia of Samara Scientific Center of the Russian Academy of Sci-ences 2014 16(4) 256ndash260 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_4_256_260pdf

14 Nizomov Z Gulov B Ganiev IN Saidov RH Obidov FU Es-hov BB Research of temperature dependence special heat capacity of aluminium special cleanliness and A7 Doklady AN Respubliki Tadzhikistan = Reports of the Academy of Sciences of the Republic of Tajikistan 2011 54(1) 53ndash59 (In Russ)

15 Ganiev IN Otajonov SE Ibrohimov NF Mahmudov M Tem-perature dependence of the specific heat and thermodynamic func-tions AК1М2 alloy doped strontium Izvestiya Vysshikh Uchebnykh Zavedenii Materialy Elektronnoi Tekhniki = Materials of Elec-tronics Engineering 2018 21(1) 35ndash42 (In Russ) httpsdoiorg10170731609-3577-2018-1-35-42

16 Maltsev MV Modifikatory struktury metallov i splavov [Modifiers of the structure of metals and alloys] Moscow Metallurgiya 1964 238 p (In Russ)

17 Vahobov AV Ganiev IN Strontium ndash the effective modifier of silu-min Liteinoe proizvodstvo = Foundry Technologies and Equipment 2000 (5) 28ndash29 (In Russ)

18 Kargapolova TB Makhmadulloev HA Ganiev IN Khakdodov MM Barium a new inoculant for silumins Liteinoe proizvodstvo = Foundry Technologies and Equipment 2001 (10) 6ndash9 (In Russ)

Modern Electronic Materials 2020 6(1) 25ndash30 27

The process of heat transfer from a hotter body to a colder one tends to establish a thermodynamic equilibri-um in a system consisting of an extremely large number of particles Therefore this is a relaxation process which can be described by an exponential function of time In the case in question the heated body transfers heat to the environment ie a body having an infinitely large heat capacity The ambient temperature can therefore be ta-ken to be constant (T0) Then the body temperature de-pendence on time τ can be written in the following form ∆T = ∆T1e

-ττ1 where ∆T is the difference between the tem-peratures of the heated body and the environment ∆T1 is the difference between the temperatures of the heated body and the environment at τ = 0 τ1 is the cooling con-stant which is equal to the time during which the differen-ce between the temperatures of the heated body and the environment decreases by e times

Schematic of the heat capacity measurement unit used in our experiment is shown in Fig 1 The electric furnace 3 is movably mounted on the platform 6 along which it can move up and down on thread The sample 4 and the stan-dard 5 which are also movable are in the form of 30 mm long 16 mm diam cylinders with channels drilled out in the butt ends in which thermocouples are inserted The ends of the thermocouples are connected to a Digital Mul-timeter DI9208L multichannel digital thermometer (7) The electric furnace 3 is powered on from the laboratory transformer 1 after setting the required temperature with the thermocontroller 2 The initial temperature is read on the multichannel digital thermometer 7 The sample 4 and the standard 5 are put into the electric furnace 3 and heated to the required temperature the latter being conrtolled with the multichannel digital thermometer 7 and the PC 8 The sample 4 and the standard 5 are simultaneously removed from the electric furnace 3 following which the tempera-ture is recorded The readings of the multichannel digital thermometer 7 are recorded with the PC 8 at 5 10 and 20 sec intervals until the sample and the standard cool down

The multichannel digital thermometer used for tempe-rature measurements allowed PC recording of measure-

ment results in a tabular form The temperature measure-ment accuracy was 01 degC the temperature recording time interval being 1 sec The relative temperature measure-ment error in the 40 to 400 degC was plusmn1 The heat capa-city measurement error for this method was within 4ndash6 depending on temperature

The measurement results were processed with MS Ex-cel and data charts were built with Sigma Plot The corre-lation coefficient was Rcorr gt 0999 confirming the correct choice of approximating function

3 Results and discussion

The experimental temperature vs time curves of the sam-ples (Fig 2) can be described with an equation of the fol-lowing type

b kT ae pe (1)

where a b p and k are constants and τ is the cooling timeDifferentiating Eq (1) with respect to τ we obtained

the following sample cooling rate equation

(2)

From Eq (2) we calculated the cooling rates of the E-AlMgSi (Aldrey) alloy samples doped with gallium (Fig 3) The values of the a b p k ab and pk coef-ficients in Eq (2) for the test alloys are summarized in Table 1

Table 1 a b p k ab and pk coefficients in Eq (2) for E-AlMgSi (Aldrey) alloy with gallium

Gallium content in E-AlMgSi (Aldrey) alloy wt

a К b 10-3 s-1

p K k 10-5 s-1

ab 10-1 Ks

pk 10-3 Ks

0 16561 446 31472 227 738 714005 17218 455 31499 220 783 69201 15914 471 31485 202 749 63505 15382 464 31399 181 713 56710 159234 473 31517 210 754 662Standard (Al Grade A5N) 49426 501 31992 257 025 823

Figure 1 Solid body ldquocoolingrdquo mode heat capacity measurement unit 1 automatic transformer 2 thermocontroller 3 electric fur-nace 4 sample 5 standard 6 electric furnace platform 7 multichannel digital thermometer and 8 recording device (PC)

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)28

Then based on the calculated alloy cooling rates and using Eq (3) we determined the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gallium and the standard (Al Grade A5N)

P PC Cmm

dTddTd

0 0 1

2

1

2

2 1= sdot

τ

τ

(3)

where m1 = ρ1V1 is the standard weight m2 = ρ2V2 is the test sample weight are the cooling rates of the al-loy and standard samples at the specific test temperature

Applying a polynomial regression we obtained the tem-perature dependence equation of the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gallium

(4)

The values of the а b c and d coefficients in Eq (4) are summarized in Table 2

Results of heat capacity calculations for the alloys using Eq (3) for different temperatures are summarized in Table 3 The heat capacity of the alloys increases with an increase in the gallium concentration in the E-AlMgSi (Aldrey) alloy and temperature Using the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gal-lium and the experimental data on the cooling rate we cal-culated the temperature dependence of the heat conducti-vity coefficient of the E-AlMgSi (Aldrey) alloy using the following equation

0

0

STTdd TmC

aP

(5)

where Т and Т0 are the sample and environment tempera-tures respectively and S and m are the surface area and weight of the sample The temperature dependences of the heat conductivity coefficient for the E-AlMgSi (Ald-rey) alloy doped with gallium are shown in Fig 4

To calculate the temperature dependence of the ent-halpy H entropy S and Gibbs energy G we used integral specific heat capacities (Eq 4)

)(4

)(3

)(2

)() ]()([ 40

430

20

200

00 TTdTTcTTbTTaTHTH (6)Figure 3 Temperature dependences of cooling rate for (1) stan-dard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium contents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Table 2 Values of the a b c and d coefficients in Eq (4) for samples of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey) alloy wt

а b с d R J(kgmiddotK) J(kgmiddotK 2) J(kgmiddotK 3) J(kgmiddotK 4)

0 -1039496 8430 021 171 09925005 -1039496 8290 -020 166 0989901 -1378822 10685 -026 211 0995005 -1946350 15221 -038 315 0998010 -1014732 7849 -019 151 09989Standard (Al Grade A5N) 64588 036 0 0 10

R is the correlation coefficient

Figure 4 Temperature dependences of heat conductivity co-efficient for (1) standard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium con-tents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Figure 2 Temperature as a function of cooling time for (1) standard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium contents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Modern Electronic Materials 2020 6(1) 25ndash30 29

)(3

)(2

)(l n) ]()([ 30

320

20

00

00 TTdTTcTTbTTaTSTS (7)

)]()([) ]()([) ]()([ 000

000

000 TSTSTTHTHTGTG (8)

where T0 = 29815 KResults of enthalpy entropy and Gibbs energy calcula-

tions using Eqs (6)ndash(8) with a 25 K step are summarized in Table 4

Table 3 Temperature dependence of specific heat capacity (kJ(kgmiddotK)) of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey) alloy wt 0

0PC kJ(kg middot K)

300 K 325 K 350 K 375 K 400 K 450 K0 75100 85536 90762 92383 92000 91637005 67855 79412 85813 88615 89372 9098001 57454 73123 82021 86125 87413 8945505 53177 71259 80269 83160 82886 8465310 53162 65839 73381 77205 78726 80520Standard (Al Grade A5N) 85462 87790 90155 92545 94948 99746

Table 4 Temperature dependences of thermodynamic functions of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey)

alloy wt

Thermodynamic Functions 300 K 325 K 350 K 375 K 400 K 450 K

[H 0(T ) ndash H 0 (T0) ] kJkg for alloys

0 13799 215847 437138 666654 897383 1354471005 12451 197762 405196 623809 846546 129562601 11125 184786 389238 609993 837508 129937205 09674 167417 358409 563663 771572 118585210 09726 159695 334642 523503 718750 1115986Standard (Al Grade A5N) 15795 232351 454777 683149 917514 1404266[S 0(T ) ndash S 0 (T0

) ] kJ(kgmiddotK) for alloys0 00046 00692 01348 01982 02577 03654005 00042 00634 01248 01852 02427 0348401 00037 00592 01198 01807 02394 0348205 00033 00536 01102 01669 02205 0318110 00033 00512 01030 01551 02055 02991Standard (Al Grade A5N) 00053 00746 01405 02035 02640 03786[G 0(T ) ndash G 0 (T0

) ] kJkg for alloys0 -00043 -09209 -34739 -76429 -133499 -289837005 -00038 -08394 -31931 -70741 -124299 -27254901 -00034 -07732 -30065 -67655 -120232 -26757605 -00031 -06922 -27354 -62028 -110526 -24559510 -00030 -06705 -25947 -58237 -103367 -229901Standard (Al Grade A5N) -00049 -10111 -37068 -80133 -138629 -299625T0 = 29815 K

Figure 5 Microstructure (times650) of E-AlMgSi (Aldrey) alloy (a) pure and (bndashe) doped with gallium wt (a) 0 (b) 005 (c) 01 (d) 05 and (e) 10

c

a

e

b

d

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)30

The increase in the enthalpy entropy and Gibbs energy of the E-AlMgSi (Aldrey) alloy upon gallium doping can be accounted for by an increase in the heterogeneity of the structure of the alloys [16ndash18] As can be seen from Fig 5d e the microstructure of the E-AlMgSi (Ald-rey) alloy containing 05 and 10 wt gallium does not exhibit primary Mg2Si precipitates In the initial alloy (Fig 5a) and low-gallium alloys (Fig 5b c) the Mg2Si phase precipitates crystallize in a needle-shaped form in the aluminum solid solution matrix

4 Conclusion

The heat capacity of the AlMgSi (Aldrey) alloy doped with gallium was determined in ldquocoolingrdquo mode based

on the known heat capacity of a A5N aluminum stan-dard Using the obtained polynomial dependences we showed that with an increase in temperature the heat ca-pacity enthalpy and entropy of the alloys increase and the Gibbs energy decreases Gallium doping within the experimental concentration range (005ndash10 wt) redu-ce the heat capacity enthalpy and entropy of the initial AlMgSi (Aldrey) alloy but increase the Gibbs energy The increase in the heat capacity heat conductivity en-thalpy and entropy of the alloys with gallium content is accounted for by the modifying action of gallium on the structure of the α-Al solid solution and hence an in-crease in the heterogeneity of the structure of the multi-component alloys

References1 Usov VV Zaimovsky AS Provodnikovye reostatnye i kontaktnye

materialy Materialy i splavy v elektrotekhnike [Conductor rheostat and contact materials Materials and alloys in electrical engineering] Vol 2 Moscow Leningrad Gosenergoizdat 1957 184 p (In Russ)

2 Alyuminievye splavy svoistva obrabotka primenenie [Aluminum alloys properties processing application] Moscow Metallurgy 1979 679 p (In Russ)

3 Alieva SG Altman MB Ambartsumyan SM et al Promyshlen-nye alyuminievye splavy Spravochnik [Industrial aluminum alloys Handbook] Moscow Metallurgy 1984 528 p (In Russ)

4 Beleskiy VM Krivov GA Alyuminievye splavy (Sostav svoistva tekh-nologiya primenenie) [Aluminum alloys (Composition properties technology application)] Kiev KOMITEKh 2005 365 p (In Russ)

5 Chlistovsky RM Heffernan PJ DuQuesnay DL Corrosion-fatigue behaviour of 7075-T651 aluminum alloy subjected to periodic over-loads Internat J Fatigue 2007 29(9ndash11) 1941ndash1949 httpsdoiorg101016jijfatigue200701010

6 Luts AR Suslina AA Alyuminii i ego splavy [Aluminum and its alloys] Samara Samara State Technical University 2013 81 p (In Russ)

7 Niezov KhKh Ganiev IN Berdiev AE Splavy osobochistogo al-yuminiya s redkozemelrsquonymi metallami [Alloys high purity alumin-ium with rare-earth metals] Dushanbe Sarmad kompaniya 2017 146 p (In Russ)

8 Berdiev AE Ganiev IN Niyozov HH Obidov FU Ismoilov RA Influence of yttrium on the anodic behavior of the alloy AK1M2 Iz-vestiya vuzov Izvestiya vuzov Materialy elektronnoi tekhniki = Ma-terials of Electronics Engineering 2014 17(3) 224ndash227 (In Russ) httpsdoiorg10170731609-3577-2014-3-224-227

9 Ganiev IN Mulloeva NM Nizomov Z Obidov FU Ibragimov NF Temperature dependence of the specific heat and thermodynam-ic functions of alloys of the Pb-Ca system High Temperature 2014 52(1) 138ndash140 httpsdoiorg101134S0018151X1401009X

10 Ganiev IN Mulloeva NM Nizomov ZA Makhmadulloev HA Heatphyscal properties and thermodynamic functions alloys of Pb-Sr system Izvestiya Samarskogo nauchno tsentra Rossiiskoi Aka-demii nauk = Izvestia of Samara Scientific Center of the Russian

Academy of Sciences 2014 6(6) 38ndash42 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_6_38_42pdf

11 Ibrokhimov NF Ganiev IN Nizomov Z Ganieva NI Ibrokh-imov SZh Effect of cerium on the thermophysical properties of AMg2 alloy The Physics of Metals and Metallography 2016 117(1) 49ndash53 httpsdoiorg101134S0031918X16010063

12 Ganiev IN Yakubov USh Sangov MM Safarov AG Calcium influence upon the temperature dependence of specific heat capacity and on changes in the thermodynamic functions of aluminum alloy AlFe5S10 Vestnik tekhnologicheskogo universiteta = Bulletin of the Technological University 2018 21(8) 11ndash15 (In Russ)

13 Ibrohimov SZh Eshov BB Ganiev IN Ibrohimov NF Influence scandium on the physicochemical properties of the alloy AMg4 Iz-vestiya Samarskogo nauchno tsentra Rossiiskoi Akademii nauk = Izvestia of Samara Scientific Center of the Russian Academy of Sci-ences 2014 16(4) 256ndash260 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_4_256_260pdf

14 Nizomov Z Gulov B Ganiev IN Saidov RH Obidov FU Es-hov BB Research of temperature dependence special heat capacity of aluminium special cleanliness and A7 Doklady AN Respubliki Tadzhikistan = Reports of the Academy of Sciences of the Republic of Tajikistan 2011 54(1) 53ndash59 (In Russ)

15 Ganiev IN Otajonov SE Ibrohimov NF Mahmudov M Tem-perature dependence of the specific heat and thermodynamic func-tions AК1М2 alloy doped strontium Izvestiya Vysshikh Uchebnykh Zavedenii Materialy Elektronnoi Tekhniki = Materials of Elec-tronics Engineering 2018 21(1) 35ndash42 (In Russ) httpsdoiorg10170731609-3577-2018-1-35-42

16 Maltsev MV Modifikatory struktury metallov i splavov [Modifiers of the structure of metals and alloys] Moscow Metallurgiya 1964 238 p (In Russ)

17 Vahobov AV Ganiev IN Strontium ndash the effective modifier of silu-min Liteinoe proizvodstvo = Foundry Technologies and Equipment 2000 (5) 28ndash29 (In Russ)

18 Kargapolova TB Makhmadulloev HA Ganiev IN Khakdodov MM Barium a new inoculant for silumins Liteinoe proizvodstvo = Foundry Technologies and Equipment 2001 (10) 6ndash9 (In Russ)

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)28

Then based on the calculated alloy cooling rates and using Eq (3) we determined the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gallium and the standard (Al Grade A5N)

P PC Cmm

dTddTd

0 0 1

2

1

2

2 1= sdot

τ

τ

(3)

where m1 = ρ1V1 is the standard weight m2 = ρ2V2 is the test sample weight are the cooling rates of the al-loy and standard samples at the specific test temperature

Applying a polynomial regression we obtained the tem-perature dependence equation of the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gallium

(4)

The values of the а b c and d coefficients in Eq (4) are summarized in Table 2

Results of heat capacity calculations for the alloys using Eq (3) for different temperatures are summarized in Table 3 The heat capacity of the alloys increases with an increase in the gallium concentration in the E-AlMgSi (Aldrey) alloy and temperature Using the specific heat capacity of the E-AlMgSi (Aldrey) alloy doped with gal-lium and the experimental data on the cooling rate we cal-culated the temperature dependence of the heat conducti-vity coefficient of the E-AlMgSi (Aldrey) alloy using the following equation

0

0

STTdd TmC

aP

(5)

where Т and Т0 are the sample and environment tempera-tures respectively and S and m are the surface area and weight of the sample The temperature dependences of the heat conductivity coefficient for the E-AlMgSi (Ald-rey) alloy doped with gallium are shown in Fig 4

To calculate the temperature dependence of the ent-halpy H entropy S and Gibbs energy G we used integral specific heat capacities (Eq 4)

)(4

)(3

)(2

)() ]()([ 40

430

20

200

00 TTdTTcTTbTTaTHTH (6)Figure 3 Temperature dependences of cooling rate for (1) stan-dard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium contents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Table 2 Values of the a b c and d coefficients in Eq (4) for samples of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey) alloy wt

а b с d R J(kgmiddotK) J(kgmiddotK 2) J(kgmiddotK 3) J(kgmiddotK 4)

0 -1039496 8430 021 171 09925005 -1039496 8290 -020 166 0989901 -1378822 10685 -026 211 0995005 -1946350 15221 -038 315 0998010 -1014732 7849 -019 151 09989Standard (Al Grade A5N) 64588 036 0 0 10

R is the correlation coefficient

Figure 4 Temperature dependences of heat conductivity co-efficient for (1) standard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium con-tents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Figure 2 Temperature as a function of cooling time for (1) standard (aluminum Grade A5N) and (2ndash6) E-AlMgSi (Aldrey) alloy samples with different gallium contents wt (2) 0 (3) 005 (4) 01 (5) 05 and (6) 10

Modern Electronic Materials 2020 6(1) 25ndash30 29

)(3

)(2

)(l n) ]()([ 30

320

20

00

00 TTdTTcTTbTTaTSTS (7)

)]()([) ]()([) ]()([ 000

000

000 TSTSTTHTHTGTG (8)

where T0 = 29815 KResults of enthalpy entropy and Gibbs energy calcula-

tions using Eqs (6)ndash(8) with a 25 K step are summarized in Table 4

Table 3 Temperature dependence of specific heat capacity (kJ(kgmiddotK)) of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey) alloy wt 0

0PC kJ(kg middot K)

300 K 325 K 350 K 375 K 400 K 450 K0 75100 85536 90762 92383 92000 91637005 67855 79412 85813 88615 89372 9098001 57454 73123 82021 86125 87413 8945505 53177 71259 80269 83160 82886 8465310 53162 65839 73381 77205 78726 80520Standard (Al Grade A5N) 85462 87790 90155 92545 94948 99746

Table 4 Temperature dependences of thermodynamic functions of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey)

alloy wt

Thermodynamic Functions 300 K 325 K 350 K 375 K 400 K 450 K

[H 0(T ) ndash H 0 (T0) ] kJkg for alloys

0 13799 215847 437138 666654 897383 1354471005 12451 197762 405196 623809 846546 129562601 11125 184786 389238 609993 837508 129937205 09674 167417 358409 563663 771572 118585210 09726 159695 334642 523503 718750 1115986Standard (Al Grade A5N) 15795 232351 454777 683149 917514 1404266[S 0(T ) ndash S 0 (T0

) ] kJ(kgmiddotK) for alloys0 00046 00692 01348 01982 02577 03654005 00042 00634 01248 01852 02427 0348401 00037 00592 01198 01807 02394 0348205 00033 00536 01102 01669 02205 0318110 00033 00512 01030 01551 02055 02991Standard (Al Grade A5N) 00053 00746 01405 02035 02640 03786[G 0(T ) ndash G 0 (T0

) ] kJkg for alloys0 -00043 -09209 -34739 -76429 -133499 -289837005 -00038 -08394 -31931 -70741 -124299 -27254901 -00034 -07732 -30065 -67655 -120232 -26757605 -00031 -06922 -27354 -62028 -110526 -24559510 -00030 -06705 -25947 -58237 -103367 -229901Standard (Al Grade A5N) -00049 -10111 -37068 -80133 -138629 -299625T0 = 29815 K

Figure 5 Microstructure (times650) of E-AlMgSi (Aldrey) alloy (a) pure and (bndashe) doped with gallium wt (a) 0 (b) 005 (c) 01 (d) 05 and (e) 10

c

a

e

b

d

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)30

The increase in the enthalpy entropy and Gibbs energy of the E-AlMgSi (Aldrey) alloy upon gallium doping can be accounted for by an increase in the heterogeneity of the structure of the alloys [16ndash18] As can be seen from Fig 5d e the microstructure of the E-AlMgSi (Ald-rey) alloy containing 05 and 10 wt gallium does not exhibit primary Mg2Si precipitates In the initial alloy (Fig 5a) and low-gallium alloys (Fig 5b c) the Mg2Si phase precipitates crystallize in a needle-shaped form in the aluminum solid solution matrix

4 Conclusion

The heat capacity of the AlMgSi (Aldrey) alloy doped with gallium was determined in ldquocoolingrdquo mode based

on the known heat capacity of a A5N aluminum stan-dard Using the obtained polynomial dependences we showed that with an increase in temperature the heat ca-pacity enthalpy and entropy of the alloys increase and the Gibbs energy decreases Gallium doping within the experimental concentration range (005ndash10 wt) redu-ce the heat capacity enthalpy and entropy of the initial AlMgSi (Aldrey) alloy but increase the Gibbs energy The increase in the heat capacity heat conductivity en-thalpy and entropy of the alloys with gallium content is accounted for by the modifying action of gallium on the structure of the α-Al solid solution and hence an in-crease in the heterogeneity of the structure of the multi-component alloys

References1 Usov VV Zaimovsky AS Provodnikovye reostatnye i kontaktnye

materialy Materialy i splavy v elektrotekhnike [Conductor rheostat and contact materials Materials and alloys in electrical engineering] Vol 2 Moscow Leningrad Gosenergoizdat 1957 184 p (In Russ)

2 Alyuminievye splavy svoistva obrabotka primenenie [Aluminum alloys properties processing application] Moscow Metallurgy 1979 679 p (In Russ)

3 Alieva SG Altman MB Ambartsumyan SM et al Promyshlen-nye alyuminievye splavy Spravochnik [Industrial aluminum alloys Handbook] Moscow Metallurgy 1984 528 p (In Russ)

4 Beleskiy VM Krivov GA Alyuminievye splavy (Sostav svoistva tekh-nologiya primenenie) [Aluminum alloys (Composition properties technology application)] Kiev KOMITEKh 2005 365 p (In Russ)

5 Chlistovsky RM Heffernan PJ DuQuesnay DL Corrosion-fatigue behaviour of 7075-T651 aluminum alloy subjected to periodic over-loads Internat J Fatigue 2007 29(9ndash11) 1941ndash1949 httpsdoiorg101016jijfatigue200701010

6 Luts AR Suslina AA Alyuminii i ego splavy [Aluminum and its alloys] Samara Samara State Technical University 2013 81 p (In Russ)

7 Niezov KhKh Ganiev IN Berdiev AE Splavy osobochistogo al-yuminiya s redkozemelrsquonymi metallami [Alloys high purity alumin-ium with rare-earth metals] Dushanbe Sarmad kompaniya 2017 146 p (In Russ)

8 Berdiev AE Ganiev IN Niyozov HH Obidov FU Ismoilov RA Influence of yttrium on the anodic behavior of the alloy AK1M2 Iz-vestiya vuzov Izvestiya vuzov Materialy elektronnoi tekhniki = Ma-terials of Electronics Engineering 2014 17(3) 224ndash227 (In Russ) httpsdoiorg10170731609-3577-2014-3-224-227

9 Ganiev IN Mulloeva NM Nizomov Z Obidov FU Ibragimov NF Temperature dependence of the specific heat and thermodynam-ic functions of alloys of the Pb-Ca system High Temperature 2014 52(1) 138ndash140 httpsdoiorg101134S0018151X1401009X

10 Ganiev IN Mulloeva NM Nizomov ZA Makhmadulloev HA Heatphyscal properties and thermodynamic functions alloys of Pb-Sr system Izvestiya Samarskogo nauchno tsentra Rossiiskoi Aka-demii nauk = Izvestia of Samara Scientific Center of the Russian

Academy of Sciences 2014 6(6) 38ndash42 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_6_38_42pdf

11 Ibrokhimov NF Ganiev IN Nizomov Z Ganieva NI Ibrokh-imov SZh Effect of cerium on the thermophysical properties of AMg2 alloy The Physics of Metals and Metallography 2016 117(1) 49ndash53 httpsdoiorg101134S0031918X16010063

12 Ganiev IN Yakubov USh Sangov MM Safarov AG Calcium influence upon the temperature dependence of specific heat capacity and on changes in the thermodynamic functions of aluminum alloy AlFe5S10 Vestnik tekhnologicheskogo universiteta = Bulletin of the Technological University 2018 21(8) 11ndash15 (In Russ)

13 Ibrohimov SZh Eshov BB Ganiev IN Ibrohimov NF Influence scandium on the physicochemical properties of the alloy AMg4 Iz-vestiya Samarskogo nauchno tsentra Rossiiskoi Akademii nauk = Izvestia of Samara Scientific Center of the Russian Academy of Sci-ences 2014 16(4) 256ndash260 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_4_256_260pdf

14 Nizomov Z Gulov B Ganiev IN Saidov RH Obidov FU Es-hov BB Research of temperature dependence special heat capacity of aluminium special cleanliness and A7 Doklady AN Respubliki Tadzhikistan = Reports of the Academy of Sciences of the Republic of Tajikistan 2011 54(1) 53ndash59 (In Russ)

15 Ganiev IN Otajonov SE Ibrohimov NF Mahmudov M Tem-perature dependence of the specific heat and thermodynamic func-tions AК1М2 alloy doped strontium Izvestiya Vysshikh Uchebnykh Zavedenii Materialy Elektronnoi Tekhniki = Materials of Elec-tronics Engineering 2018 21(1) 35ndash42 (In Russ) httpsdoiorg10170731609-3577-2018-1-35-42

16 Maltsev MV Modifikatory struktury metallov i splavov [Modifiers of the structure of metals and alloys] Moscow Metallurgiya 1964 238 p (In Russ)

17 Vahobov AV Ganiev IN Strontium ndash the effective modifier of silu-min Liteinoe proizvodstvo = Foundry Technologies and Equipment 2000 (5) 28ndash29 (In Russ)

18 Kargapolova TB Makhmadulloev HA Ganiev IN Khakdodov MM Barium a new inoculant for silumins Liteinoe proizvodstvo = Foundry Technologies and Equipment 2001 (10) 6ndash9 (In Russ)

Modern Electronic Materials 2020 6(1) 25ndash30 29

)(3

)(2

)(l n) ]()([ 30

320

20

00

00 TTdTTcTTbTTaTSTS (7)

)]()([) ]()([) ]()([ 000

000

000 TSTSTTHTHTGTG (8)

where T0 = 29815 KResults of enthalpy entropy and Gibbs energy calcula-

tions using Eqs (6)ndash(8) with a 25 K step are summarized in Table 4

Table 3 Temperature dependence of specific heat capacity (kJ(kgmiddotK)) of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey) alloy wt 0

0PC kJ(kg middot K)

300 K 325 K 350 K 375 K 400 K 450 K0 75100 85536 90762 92383 92000 91637005 67855 79412 85813 88615 89372 9098001 57454 73123 82021 86125 87413 8945505 53177 71259 80269 83160 82886 8465310 53162 65839 73381 77205 78726 80520Standard (Al Grade A5N) 85462 87790 90155 92545 94948 99746

Table 4 Temperature dependences of thermodynamic functions of E-AlMgSi (Aldrey) alloy doped with gallium and standard (Al Grade A5N)

Gallium content in E-AlMgSi (Aldrey)

alloy wt

Thermodynamic Functions 300 K 325 K 350 K 375 K 400 K 450 K

[H 0(T ) ndash H 0 (T0) ] kJkg for alloys

0 13799 215847 437138 666654 897383 1354471005 12451 197762 405196 623809 846546 129562601 11125 184786 389238 609993 837508 129937205 09674 167417 358409 563663 771572 118585210 09726 159695 334642 523503 718750 1115986Standard (Al Grade A5N) 15795 232351 454777 683149 917514 1404266[S 0(T ) ndash S 0 (T0

) ] kJ(kgmiddotK) for alloys0 00046 00692 01348 01982 02577 03654005 00042 00634 01248 01852 02427 0348401 00037 00592 01198 01807 02394 0348205 00033 00536 01102 01669 02205 0318110 00033 00512 01030 01551 02055 02991Standard (Al Grade A5N) 00053 00746 01405 02035 02640 03786[G 0(T ) ndash G 0 (T0

) ] kJkg for alloys0 -00043 -09209 -34739 -76429 -133499 -289837005 -00038 -08394 -31931 -70741 -124299 -27254901 -00034 -07732 -30065 -67655 -120232 -26757605 -00031 -06922 -27354 -62028 -110526 -24559510 -00030 -06705 -25947 -58237 -103367 -229901Standard (Al Grade A5N) -00049 -10111 -37068 -80133 -138629 -299625T0 = 29815 K

Figure 5 Microstructure (times650) of E-AlMgSi (Aldrey) alloy (a) pure and (bndashe) doped with gallium wt (a) 0 (b) 005 (c) 01 (d) 05 and (e) 10

c

a

e

b

d

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)30

The increase in the enthalpy entropy and Gibbs energy of the E-AlMgSi (Aldrey) alloy upon gallium doping can be accounted for by an increase in the heterogeneity of the structure of the alloys [16ndash18] As can be seen from Fig 5d e the microstructure of the E-AlMgSi (Ald-rey) alloy containing 05 and 10 wt gallium does not exhibit primary Mg2Si precipitates In the initial alloy (Fig 5a) and low-gallium alloys (Fig 5b c) the Mg2Si phase precipitates crystallize in a needle-shaped form in the aluminum solid solution matrix

4 Conclusion

The heat capacity of the AlMgSi (Aldrey) alloy doped with gallium was determined in ldquocoolingrdquo mode based

on the known heat capacity of a A5N aluminum stan-dard Using the obtained polynomial dependences we showed that with an increase in temperature the heat ca-pacity enthalpy and entropy of the alloys increase and the Gibbs energy decreases Gallium doping within the experimental concentration range (005ndash10 wt) redu-ce the heat capacity enthalpy and entropy of the initial AlMgSi (Aldrey) alloy but increase the Gibbs energy The increase in the heat capacity heat conductivity en-thalpy and entropy of the alloys with gallium content is accounted for by the modifying action of gallium on the structure of the α-Al solid solution and hence an in-crease in the heterogeneity of the structure of the multi-component alloys

References1 Usov VV Zaimovsky AS Provodnikovye reostatnye i kontaktnye

materialy Materialy i splavy v elektrotekhnike [Conductor rheostat and contact materials Materials and alloys in electrical engineering] Vol 2 Moscow Leningrad Gosenergoizdat 1957 184 p (In Russ)

2 Alyuminievye splavy svoistva obrabotka primenenie [Aluminum alloys properties processing application] Moscow Metallurgy 1979 679 p (In Russ)

3 Alieva SG Altman MB Ambartsumyan SM et al Promyshlen-nye alyuminievye splavy Spravochnik [Industrial aluminum alloys Handbook] Moscow Metallurgy 1984 528 p (In Russ)

4 Beleskiy VM Krivov GA Alyuminievye splavy (Sostav svoistva tekh-nologiya primenenie) [Aluminum alloys (Composition properties technology application)] Kiev KOMITEKh 2005 365 p (In Russ)

5 Chlistovsky RM Heffernan PJ DuQuesnay DL Corrosion-fatigue behaviour of 7075-T651 aluminum alloy subjected to periodic over-loads Internat J Fatigue 2007 29(9ndash11) 1941ndash1949 httpsdoiorg101016jijfatigue200701010

6 Luts AR Suslina AA Alyuminii i ego splavy [Aluminum and its alloys] Samara Samara State Technical University 2013 81 p (In Russ)

7 Niezov KhKh Ganiev IN Berdiev AE Splavy osobochistogo al-yuminiya s redkozemelrsquonymi metallami [Alloys high purity alumin-ium with rare-earth metals] Dushanbe Sarmad kompaniya 2017 146 p (In Russ)

8 Berdiev AE Ganiev IN Niyozov HH Obidov FU Ismoilov RA Influence of yttrium on the anodic behavior of the alloy AK1M2 Iz-vestiya vuzov Izvestiya vuzov Materialy elektronnoi tekhniki = Ma-terials of Electronics Engineering 2014 17(3) 224ndash227 (In Russ) httpsdoiorg10170731609-3577-2014-3-224-227

9 Ganiev IN Mulloeva NM Nizomov Z Obidov FU Ibragimov NF Temperature dependence of the specific heat and thermodynam-ic functions of alloys of the Pb-Ca system High Temperature 2014 52(1) 138ndash140 httpsdoiorg101134S0018151X1401009X

10 Ganiev IN Mulloeva NM Nizomov ZA Makhmadulloev HA Heatphyscal properties and thermodynamic functions alloys of Pb-Sr system Izvestiya Samarskogo nauchno tsentra Rossiiskoi Aka-demii nauk = Izvestia of Samara Scientific Center of the Russian

Academy of Sciences 2014 6(6) 38ndash42 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_6_38_42pdf

11 Ibrokhimov NF Ganiev IN Nizomov Z Ganieva NI Ibrokh-imov SZh Effect of cerium on the thermophysical properties of AMg2 alloy The Physics of Metals and Metallography 2016 117(1) 49ndash53 httpsdoiorg101134S0031918X16010063

12 Ganiev IN Yakubov USh Sangov MM Safarov AG Calcium influence upon the temperature dependence of specific heat capacity and on changes in the thermodynamic functions of aluminum alloy AlFe5S10 Vestnik tekhnologicheskogo universiteta = Bulletin of the Technological University 2018 21(8) 11ndash15 (In Russ)

13 Ibrohimov SZh Eshov BB Ganiev IN Ibrohimov NF Influence scandium on the physicochemical properties of the alloy AMg4 Iz-vestiya Samarskogo nauchno tsentra Rossiiskoi Akademii nauk = Izvestia of Samara Scientific Center of the Russian Academy of Sci-ences 2014 16(4) 256ndash260 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_4_256_260pdf

14 Nizomov Z Gulov B Ganiev IN Saidov RH Obidov FU Es-hov BB Research of temperature dependence special heat capacity of aluminium special cleanliness and A7 Doklady AN Respubliki Tadzhikistan = Reports of the Academy of Sciences of the Republic of Tajikistan 2011 54(1) 53ndash59 (In Russ)

15 Ganiev IN Otajonov SE Ibrohimov NF Mahmudov M Tem-perature dependence of the specific heat and thermodynamic func-tions AК1М2 alloy doped strontium Izvestiya Vysshikh Uchebnykh Zavedenii Materialy Elektronnoi Tekhniki = Materials of Elec-tronics Engineering 2018 21(1) 35ndash42 (In Russ) httpsdoiorg10170731609-3577-2018-1-35-42

16 Maltsev MV Modifikatory struktury metallov i splavov [Modifiers of the structure of metals and alloys] Moscow Metallurgiya 1964 238 p (In Russ)

17 Vahobov AV Ganiev IN Strontium ndash the effective modifier of silu-min Liteinoe proizvodstvo = Foundry Technologies and Equipment 2000 (5) 28ndash29 (In Russ)

18 Kargapolova TB Makhmadulloev HA Ganiev IN Khakdodov MM Barium a new inoculant for silumins Liteinoe proizvodstvo = Foundry Technologies and Equipment 2001 (10) 6ndash9 (In Russ)

Ganiev IN et al Heat capacity and thermodynamic functions of E-AlMgSi (Aldrey)30

The increase in the enthalpy entropy and Gibbs energy of the E-AlMgSi (Aldrey) alloy upon gallium doping can be accounted for by an increase in the heterogeneity of the structure of the alloys [16ndash18] As can be seen from Fig 5d e the microstructure of the E-AlMgSi (Ald-rey) alloy containing 05 and 10 wt gallium does not exhibit primary Mg2Si precipitates In the initial alloy (Fig 5a) and low-gallium alloys (Fig 5b c) the Mg2Si phase precipitates crystallize in a needle-shaped form in the aluminum solid solution matrix

4 Conclusion

The heat capacity of the AlMgSi (Aldrey) alloy doped with gallium was determined in ldquocoolingrdquo mode based

on the known heat capacity of a A5N aluminum stan-dard Using the obtained polynomial dependences we showed that with an increase in temperature the heat ca-pacity enthalpy and entropy of the alloys increase and the Gibbs energy decreases Gallium doping within the experimental concentration range (005ndash10 wt) redu-ce the heat capacity enthalpy and entropy of the initial AlMgSi (Aldrey) alloy but increase the Gibbs energy The increase in the heat capacity heat conductivity en-thalpy and entropy of the alloys with gallium content is accounted for by the modifying action of gallium on the structure of the α-Al solid solution and hence an in-crease in the heterogeneity of the structure of the multi-component alloys

References1 Usov VV Zaimovsky AS Provodnikovye reostatnye i kontaktnye

materialy Materialy i splavy v elektrotekhnike [Conductor rheostat and contact materials Materials and alloys in electrical engineering] Vol 2 Moscow Leningrad Gosenergoizdat 1957 184 p (In Russ)

2 Alyuminievye splavy svoistva obrabotka primenenie [Aluminum alloys properties processing application] Moscow Metallurgy 1979 679 p (In Russ)

3 Alieva SG Altman MB Ambartsumyan SM et al Promyshlen-nye alyuminievye splavy Spravochnik [Industrial aluminum alloys Handbook] Moscow Metallurgy 1984 528 p (In Russ)

4 Beleskiy VM Krivov GA Alyuminievye splavy (Sostav svoistva tekh-nologiya primenenie) [Aluminum alloys (Composition properties technology application)] Kiev KOMITEKh 2005 365 p (In Russ)

5 Chlistovsky RM Heffernan PJ DuQuesnay DL Corrosion-fatigue behaviour of 7075-T651 aluminum alloy subjected to periodic over-loads Internat J Fatigue 2007 29(9ndash11) 1941ndash1949 httpsdoiorg101016jijfatigue200701010

6 Luts AR Suslina AA Alyuminii i ego splavy [Aluminum and its alloys] Samara Samara State Technical University 2013 81 p (In Russ)

7 Niezov KhKh Ganiev IN Berdiev AE Splavy osobochistogo al-yuminiya s redkozemelrsquonymi metallami [Alloys high purity alumin-ium with rare-earth metals] Dushanbe Sarmad kompaniya 2017 146 p (In Russ)

8 Berdiev AE Ganiev IN Niyozov HH Obidov FU Ismoilov RA Influence of yttrium on the anodic behavior of the alloy AK1M2 Iz-vestiya vuzov Izvestiya vuzov Materialy elektronnoi tekhniki = Ma-terials of Electronics Engineering 2014 17(3) 224ndash227 (In Russ) httpsdoiorg10170731609-3577-2014-3-224-227

9 Ganiev IN Mulloeva NM Nizomov Z Obidov FU Ibragimov NF Temperature dependence of the specific heat and thermodynam-ic functions of alloys of the Pb-Ca system High Temperature 2014 52(1) 138ndash140 httpsdoiorg101134S0018151X1401009X

10 Ganiev IN Mulloeva NM Nizomov ZA Makhmadulloev HA Heatphyscal properties and thermodynamic functions alloys of Pb-Sr system Izvestiya Samarskogo nauchno tsentra Rossiiskoi Aka-demii nauk = Izvestia of Samara Scientific Center of the Russian

Academy of Sciences 2014 6(6) 38ndash42 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_6_38_42pdf

11 Ibrokhimov NF Ganiev IN Nizomov Z Ganieva NI Ibrokh-imov SZh Effect of cerium on the thermophysical properties of AMg2 alloy The Physics of Metals and Metallography 2016 117(1) 49ndash53 httpsdoiorg101134S0031918X16010063

12 Ganiev IN Yakubov USh Sangov MM Safarov AG Calcium influence upon the temperature dependence of specific heat capacity and on changes in the thermodynamic functions of aluminum alloy AlFe5S10 Vestnik tekhnologicheskogo universiteta = Bulletin of the Technological University 2018 21(8) 11ndash15 (In Russ)

13 Ibrohimov SZh Eshov BB Ganiev IN Ibrohimov NF Influence scandium on the physicochemical properties of the alloy AMg4 Iz-vestiya Samarskogo nauchno tsentra Rossiiskoi Akademii nauk = Izvestia of Samara Scientific Center of the Russian Academy of Sci-ences 2014 16(4) 256ndash260 (In Russ) URL httpwwwsscsmrrumediajournalsizvestia20142014_4_256_260pdf

14 Nizomov Z Gulov B Ganiev IN Saidov RH Obidov FU Es-hov BB Research of temperature dependence special heat capacity of aluminium special cleanliness and A7 Doklady AN Respubliki Tadzhikistan = Reports of the Academy of Sciences of the Republic of Tajikistan 2011 54(1) 53ndash59 (In Russ)

15 Ganiev IN Otajonov SE Ibrohimov NF Mahmudov M Tem-perature dependence of the specific heat and thermodynamic func-tions AК1М2 alloy doped strontium Izvestiya Vysshikh Uchebnykh Zavedenii Materialy Elektronnoi Tekhniki = Materials of Elec-tronics Engineering 2018 21(1) 35ndash42 (In Russ) httpsdoiorg10170731609-3577-2018-1-35-42

16 Maltsev MV Modifikatory struktury metallov i splavov [Modifiers of the structure of metals and alloys] Moscow Metallurgiya 1964 238 p (In Russ)

17 Vahobov AV Ganiev IN Strontium ndash the effective modifier of silu-min Liteinoe proizvodstvo = Foundry Technologies and Equipment 2000 (5) 28ndash29 (In Russ)

18 Kargapolova TB Makhmadulloev HA Ganiev IN Khakdodov MM Barium a new inoculant for silumins Liteinoe proizvodstvo = Foundry Technologies and Equipment 2001 (10) 6ndash9 (In Russ)